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An Optimal Control Problem of Forward‐Backward Stochastic Volterra Integral Equations with State Constraints

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  • Qingmeng Wei
  • Xinling Xiao

Abstract

This paper is devoted to the stochastic optimal control problems for systems governed by forward‐backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland′s variational principle, we obtain one kind of variational inequalities. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls.

Suggested Citation

  • Qingmeng Wei & Xinling Xiao, 2014. "An Optimal Control Problem of Forward‐Backward Stochastic Volterra Integral Equations with State Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:432718
    DOI: 10.1155/2014/432718
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    References listed on IDEAS

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    1. M. I. Kamien & E. Muller, 1976. "Optimal Control with Integral State Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 469-473.
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    3. Tianxiao Wang & Yufeng Shi, 2010. "A maximum principle for forward-backward stochastic Volterra integral equations and applications in finance," Papers 1004.2206, arXiv.org.
    4. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    5. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
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